Educational Assessments (education) is playing an increasingly important core role in assessing students' academic achievements. Traditional test theory can only provide students with a total score, and cannot provide specific information about students' internal knowledge structure and learning process. Cognitively diagnostic assessment (CDA) aims to measure learners of their cognitive strengths and weaknesses in assessed skills, so as to provide immediate diagnostic information for parents and schools, plan and guide subsequent improvement of teaching strategies and objectives. CDA is completely model-based. Currently, a large number of cognitive diagnosis models (CDMs) have been proposed to satisfy the demands of the CDAs. However, most existing CDMs are only suitable for dichotomously-scored items. In the case of the dichotomously-scored items, the test manager classifies the observed responses into two categories, correct and incorrect. In practice, there are lager polytomously-scored items/data in educational and psychological tests. It is common to use Likert-type items in questionnaires. For example, an item with four response categories, such as “Strongly Dislike”, “Dislike”, “Uncertain”, and “Strongly Like”, typically has scores of 0, 1, 2 and 3, respectively. In educational achievement test, it is also common to have polytomous items where a higher response category indicates higher ability to measure. It has been recognized that, polytomous items have several advantages over dichotomous items. For example, polytomous items can provide more information for inference, and some features are easier to measure with polytomous items such as personality, attitude, motivation, interest and more. Therefore, it is very necessary to develop CDMs for polytomous data. At present, only a few polytomous CDMs have been developed to deal with polytomous items. According to the models’ different order-preserving mechanisms in forming the dichotomies of response categories, the existing polytomous CDMs can be divided into three types: (1) graded response models, based on global (or cumulative) logit, (2) partial credit models that make use of the local (or adjacent category) category logit, and (3) sequential models, based on the continuation ratio logit. This paper briefly introduces the most commonly used polytomous CDMs, including their parameterization, the meaning of the models’ parameters, the model assumptions, the applicable scope of the model and relationships between these models, so as to provide a model reference for researchers and practical users. To explore the potential of these proposed polytomous CDMs, several future research directions can be identified. First, most CDMs assume that all students use the same strategy to solve problems. Multi-strategy CDMs take into account the differences of problem solving strategies among students and help to provide more diagnostic information. Therefore, it will be an interesting direction to study the polytomous CDMs for multiple strategies. Second, the current CDMs almost only utilize information on item responses and ignores an important source of information about a respondent's behaviour, namely response times (RTs) to items. It is also worth trying to develop a diagnostic model that utilizes both item responses and RTs. Third, an interesting topic for future research would be the applying these proposed polytomous CDMs to develop polytomous cognitive diagnostic computerized adaptive testing (CD-CAT) and computerized adaptive multistage testing (MST).